The Hindu-Arabic Numerals | Page 6

of age to marry, the father of Gopa, his
intended bride, demanded an examination of the five hundred suitors,
the subjects including arithmetic, writing, the lute, and archery. Having
vanquished his rivals in all else, he is matched against Arjuna the great
arithmetician and is asked to express numbers greater than 100
kotis.[56] In reply he gave a scheme of number names as high as
10^{53}, adding that he could proceed as far as 10^{421},[57] all of
which suggests the system of Archimedes and the unsettled question of
the indebtedness of the West to the East in the realm of ancient
mathematics.[58] Sir Edwin Arnold, {16} in The Light of Asia, does
not mention this part of the contest, but he speaks of Buddha's training
at the hands of the learned Vi[s.]vamitra:
"And Viswamitra said, 'It is enough, Let us to numbers. After me repeat
Your numeration till we reach the lakh,[59] One, two, three, four, to ten,
and then by tens To hundreds, thousands.' After him the child Named
digits, decads, centuries, nor paused, The round lakh reached, but softly
murmured on, Then comes the k[=o]ti, nahut, ninnahut, Khamba,
viskhamba, abab, attata, To kumuds, gundhikas, and utpalas, By
pundar[=i]kas into padumas, Which last is how you count the utmost
grains Of Hastagiri ground to finest dust;[60] But beyond that a
numeration is, The K[=a]tha, used to count the stars of night, The
K[=o]ti-K[=a]tha, for the ocean drops; Ingga, the calculus of circulars;
Sarvanikchepa, by the which you deal With all the sands of Gunga, till

we come To Antah-Kalpas, where the unit is The sands of the ten crore
Gungas. If one seeks More comprehensive scale, th' arithmic mounts
By the Asankya, which is the tale Of all the drops that in ten thousand
years Would fall on all the worlds by daily rain; Thence unto Maha
Kalpas, by the which The gods compute their future and their past.'"
{17}
Thereupon Vi[s.]vamitra [=A]c[=a]rya[61] expresses his approval of
the task, and asks to hear the "measure of the line" as far as y[=o]jana,
the longest measure bearing name. This given, Buddha adds:
... "'And master! if it please, I shall recite how many sun-motes lie
From end to end within a y[=o]jana.' Thereat, with instant skill, the
little prince Pronounced the total of the atoms true. But Viswamitra
heard it on his face Prostrate before the boy; 'For thou,' he cried, 'Art
Teacher of thy teachers--thou, not I, Art G[=u]r[=u].'"
It is needless to say that this is far from being history. And yet it puts in
charming rhythm only what the ancient Lalitavistara relates of the
number-series of the Buddha's time. While it extends beyond all reason,
nevertheless it reveals a condition that would have been impossible
unless arithmetic had attained a considerable degree of advancement.
To this pre-Christian period belong also the Ved[=a][.n]gas, or "limbs
for supporting the Veda," part of that great branch of Hindu literature
known as Sm[r.]iti (recollection), that which was to be handed down by
tradition. Of these the sixth is known as Jyoti[s.]a (astronomy), a short
treatise of only thirty-six verses, written not earlier than 300 B.C., and
affording us some knowledge of the extent of number work in that
period.[62] The Hindus {18} also speak of eighteen ancient
Siddh[=a]ntas or astronomical works, which, though mostly lost,
confirm this evidence.[63]
As to authentic histories, however, there exist in India none relating to
the period before the Mohammedan era (622 A.D.). About all that we
know of the earlier civilization is what we glean from the two great
epics, the Mah[=a]bh[=a]rata[64] and the R[=a]m[=a]yana, from coins,

and from a few inscriptions.[65]
It is with this unsatisfactory material, then, that we have to deal in
searching for the early history of the Hindu-Arabic numerals, and the
fact that many unsolved problems exist and will continue to exist is no
longer strange when we consider the conditions. It is rather surprising
that so much has been discovered within a century, than that we are so
uncertain as to origins and dates and the early spread of the system. The
probability being that writing was not introduced into India before the
close of the fourth century B.C., and literature existing only in spoken
form prior to that period,[66] the number work was doubtless that of all
primitive peoples, palpable, merely a matter of placing sticks or
cowries or pebbles on the ground, of marking a sand-covered board, or
of cutting notches or tying cords as is still done in parts of Southern
India to-day.[67]
{19}
The early Hindu numerals[68] may be classified into three great groups,
(1) the Kharo[s.][t.]h[=i], (2) the Br[=a]hm[=i], and (3) the word and
letter forms; and these will be considered in order.
The Kharo[s.][t.]h[=i] numerals are found in inscriptions formerly
known as Bactrian, Indo-Bactrian, and